Vibrational predissociation processes

The method was found equally successful for similar processes in more complicated van der Waals systems. Schatz et al.49 studied vibrational predissociation processes of the type... 

Figure 10.7 Schematic illustration of the potential energy curves and wave functions for an atom-diatom system governing the vibrational predissociation process, q and R are the coordinates for the diatom and the van der Waals bonds, respectively. The angle between the diatom and atom is held fixed. Taken with permission from LeRoy et al. (1991).

Klemperer. Calculations by Coulson and Robertson on other hydrogen bonding systems yielded times of -10 s. While these discrepancies between theory and experiment are probably not a record, they give one pause to wonder about the factors which determine the efficiency of the vibrational predissociation process. 

Not only do the experimental vibrational predissociation lifetimes require interpretation, so do the increasingly sophisticated theoretical calculations whose results often fall out of a web of coupled differential equations or the convoluted algebra of quantum mechanics. In order to offer a qualitative overview of dynamical processes in van der Waals molecules, we shall introduce a selection rule which can provide insight into possible relaxation channels of vibrationally excited molecules. This selection rule concerns the change in a quantum number, Anj., which is to remain small for efficient vibrational predissociation processes. It bears a close analogy to the selection rules of optical spectroscopy which require small changes in quantum numbers Au, AJ, AS, etc. for efficient transitions between molecular states. Let us review the origin of the vibrational predissociation selection rule which has been developed in more detail elsewhere. ... 

The influence of rotational degrees of freedom during the vibrational predissociation process is the most difficult to model simply. In the spirit of this presentation we have used the simplest possible treatment by replacing the reduced mass n for the translational motion in eq. 6 by I/r for the rotational motion. This substitution, first used by Moore to relate the transfer of collision pair vibrational relaxation to rotational motions, involves I, the vibrating molecule moment of inertia, and r the distance between its center of mass and the vibrating atom. With CH for example, r becomes just the C-H bond length. For a diatomic molecule we... 

The straight line plotted in Fig. 3 is the lifetime for vibrational predissociation of eq. 5. The data points are from experimental measurements or close-coupling calculations. The times involved span 14 orders of magnitude. Let us explore the mechanisms of these vibrational predissociation processes. 

At first glance, classical mechanics seems to be an inappropriate theory for the description of many van der Waals (vdW) systems. In this paper, for example, we will focus mostly on XBC type vdW systems where X (usually a noble gas atom) is weakly bound to a chemically bound fragment BC (usually a diatomic molecule). The total angular momentum J = 0 vibrational predissociation process for such a system can be denoted by ... 

Here we review a theoretical model for determining the rate, t , of the vibrational predissociation process of reaction (4) or Fig. 4. This model which has been developed independently by Coulson and Robertson,Beswick and Jortner, and Ewing begins with the Golden Rule or its equivalent. 

With such a variety of vibrationally excited van der Waals molecules represented in Fig. 6 it may seem surprising that there can be a correlation of their predissociation lifetimes with anything. In order to understand this correlation and extract some useful physical insight into the vibrational predissociation process let us look again at the Golden Rule relationship of equation (5). 

Since we seek the cause of an exponential dependence of lifetimes on van der Waals molecule properties the linear dependence on fragment velocity, v j, cannot be of great importance. It must then be the matrix element which controls the wide variation in vibrational predissociation lifetimes. The functions within this matrix element are factored out in equation (18) and presented in Fig. 7 for the example of F-H B that we have just considered. The radial functions Rq and have been transfered from Fig. 5 and the coupling term, V Q pq ng of equations (14) and (15) are presented. The product of these three functions, -aSRjjj(dV/dr)RQ, is the r-dependent integrand of the Golden Rule matrix element and it reveals the most about the efficiency (or inefficiency) of the vibrational predissociation process. 

The temi action spectroscopy refers to those teclmiques that do not directly measure die absorption, but rather the consequence of photoabsorption. That is, there is some measurable change associated with the absorption process. There are several well known examples, such as photoionization spectroscopy [47], multi-photon ionization spectroscopy [48], photoacoustic spectroscopy [49], photoelectron spectroscopy [, 51], vibrational predissociation spectroscopy [ ] and optothemial spectroscopy [53, M]. These teclmiques have all been applied to vibrational spectroscopy, but only the last one will be discussed here. 

For complexes such as Ar-H2, Ar-HF and Ar-lTCl, vibrational predissociation is a very slow process and does not cause appreciable broadening of the lines in the infrared spectmm. Indeed, for Ar-ITF, ITuang et al [20] showed that... 

We can exclude a predissociation process [39] responsible for the decrease of the lifetime for three reasons, (i) Dispersed emission spectra did not show any indication of emission from the fragment monomer [40]. Thus no dissociation occurs on the time scale of the fluorescence emission, (ii) The additional excitation of the van der Waals stretching vibration in benzene-Ar does not lead to a further decrease of the lifetime, (iii) The stronger decrease of the lifetime of the 61 state in benzene-Kr would not be expeced for a predissociation process since the benzene-Kr complex is more strongly bound and has only a slightly higher density of states since the frequencies of the three van der Waals modes do not differ very much from that of benzene-Ar [41]. 

Vibrational Predissociation, in this section we discuss the case of a transition from a predissociative state to the photofragment state that occurs on a single adiabatic pes. Such processes cannot occur for diatomic molecules, but they can be observed for polyatomic systems. The transition is caused by intramolecular energy transfer, that is, by internal redistribution of vibrational energy. 

In this section we will explain the essential mechanism of vibrational predissociation by virtue of a linear atom-diatom complex such as Ar H2. Figure 12.1 illustrates the corresponding Jacobi coordinates, t In particular, we consider the excitation from the vibrational ground state of H2 to the first excited state as illustrated in Figure 12.2. The close-coupling approach in the diabatic representation, summarized in Section 3.1, provides a convenient basis for the description of this elementary process. For simplicity of presentation we assume that the coupling between the van der Waals coordinate R and the vibrational coordinate r is so weak that it suffices to include only the two lowest vibrational states, n = 0 and n = 1, in expansion (3.4) for the total wavefunction,... 

Figure 2-6. An energy level diagram showing the vibrational states of interest in the vibrational predissociation of Ar-C02. The experimental results show that the intramolecular V-V process, indicated by the diagonal arrows, is the dominant mechanism for dissociation. C02 vibrational energy levels designated (a), (b), and (c) are the Fermi diads and Fermi triad discussed in the text.

CCU- The authors found a faster predissociation process with time constants of 250 fs (vpu = 3225 cm-1) to 900 fs (vPu = 3450 cm For the subsequent reassociation a time constant of 15 ps was measured. From subsequent investigations of the probe transmission with perpendicular polarization, the authors inferred a fast delocalization of the deposited vibrationally energy along the oligomer chain confirming the findings of Ref. 78. 

E.E.Nikitin, Vibrational relaxation and vibrational predissociation as dynamical tunneling processes, Uspekhi Khimii 62,3 (1993)... 

However, the classical approach should not be used for a quantitative interpretation of the experimental results for single-quantum vibrational predissociation. The classical process, which should show the correspondence with the quantiun one, is the cleavage of a bond under a condition when the quantum of energy transferred to this bond from a diatomic fragment, hQ, is much smaller than the dissociation energy, Ej, of the bond, i.e. h l . This condition does not contradict the classical limit,... 

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